------------------------------------------------------------
                         α=3.0 —— rat195 —— 195 nodes       
------------------------------------------------------------

——————— Sun, 14 Jan 2024 05:10:59 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 196 hubs —— 1—15—14—27—28—29—16—17—18—19—20—21—34—33—32—31—30—44—43—42—41—40—53—54—55—56—57—58—71—70—69—68—67—66—79—80—81—82—83—84—97—96—95—94—93—92—105—106—107—108—109—110—122—121—120—119—118—131—132—133—134—147—148—149—150—151—152—153—166—165—164—163—162—161—175—174—173—172—159—160—146—145—144—158—157—170—171—183—184—185—186—187—188—189—190—176—177—178—179—192—191—193—194—195—182—181—180—167—168—169—156—155—154—141—140—139—138—137—136—135—123—124—125—126—127—128—129—142—143—130—117—116—115—114—113—112—111—98—99—100—101—102—103—104—91—90—89—88—87—86—85—72—73—74—75—76—77—78—65—64—63—62—61—60—59—45—46—47—48—49—50—51—52—39—38—37—36—35—22—23—24—25—26—13—12—11—10—9—8—7—6—5—4—3—2—196
total time           348.17               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             6969<=6969           subtour              11519.0              
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       8895                 n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—15—14—27—28—29—16—17—18—19—20—21—34—33—32—31—30—44—43—42—41—40—53—54—55—56—57—58—71—70—69—68—67—66—79—80—81—82—83—84—97—96—95—94—93—92—105—106—107—108—109—110—122—121—120—119—118—131—132—133—134—147—148—149—150—151—152—153—166—165—164—163—162—161—175—174—173—172—159—160—146—145—144—158—157—170—171—183—184—185—186—187—188—189—190—176—177—178—179—192—191—193—194—195—182—181—180—167—168—169—156—155—154—141—140—139—138—137—136—135—123—124—125—126—127—128—129—142—143—130—117—116—115—114—113—112—111—98—99—100—101—102—103—104—91—90—89—88—87—86—85—72—73—74—75—76—77—78—65—64—63—62—61—60—59—45—46—47—48—49—50—51—52—39—38—37—36—35—22—23—24—25—26—13—12—11—10—9—8—7—6—5—4—3—2—196

RING
1  --- 15 | cost [69.0]
2  ---  3 | cost [21.0]
2  --- 196 | cost [42.0]
3  ---  4 | cost [33.0]
4  ---  5 | cost [39.0]
5  ---  6 | cost [21.0]
6  ---  7 | cost [39.0]
7  ---  8 | cost [39.0]
8  ---  9 | cost [33.0]
9  --- 10 | cost [24.0]
10 --- 11 | cost [39.0]
11 --- 12 | cost [27.0]
12 --- 13 | cost [24.0]
13 --- 26 | cost [57.0]
14 --- 15 | cost [36.0]
14 --- 27 | cost [48.0]
16 --- 17 | cost [21.0]
16 --- 29 | cost [48.0]
17 --- 18 | cost [27.0]
18 --- 19 | cost [42.0]
19 --- 20 | cost [39.0]
20 --- 21 | cost [30.0]
21 --- 34 | cost [36.0]
22 --- 23 | cost [36.0]
22 --- 35 | cost [45.0]
23 --- 24 | cost [27.0]
24 --- 25 | cost [33.0]
25 --- 26 | cost [36.0]
27 --- 28 | cost [36.0]
28 --- 29 | cost [36.0]
30 --- 31 | cost [39.0]
30 --- 44 | cost [54.0]
31 --- 32 | cost [21.0]
32 --- 33 | cost [39.0]
33 --- 34 | cost [45.0]
35 --- 36 | cost [30.0]
36 --- 37 | cost [18.0]
37 --- 38 | cost [42.0]
38 --- 39 | cost [36.0]
39 --- 52 | cost [57.0]
40 --- 41 | cost [27.0]
40 --- 53 | cost [27.0]
41 --- 42 | cost [36.0]
42 --- 43 | cost [27.0]
43 --- 44 | cost [36.0]
45 --- 46 | cost [39.0]
45 --- 59 | cost [51.0]
46 --- 47 | cost [24.0]
47 --- 48 | cost [33.0]
48 --- 49 | cost [39.0]
49 --- 50 | cost [48.0]
50 --- 51 | cost [30.0]
51 --- 52 | cost [27.0]
53 --- 54 | cost [39.0]
54 --- 55 | cost [36.0]
55 --- 56 | cost [48.0]
56 --- 57 | cost [30.0]
57 --- 58 | cost [30.0]
58 --- 71 | cost [30.0]
59 --- 60 | cost [48.0]
60 --- 61 | cost [21.0]
61 --- 62 | cost [39.0]
62 --- 63 | cost [27.0]
63 --- 64 | cost [36.0]
64 --- 65 | cost [24.0]
65 --- 78 | cost [48.0]
66 --- 67 | cost [27.0]
66 --- 79 | cost [39.0]
67 --- 68 | cost [27.0]
68 --- 69 | cost [39.0]
69 --- 70 | cost [24.0]
70 --- 71 | cost [45.0]
72 --- 73 | cost [27.0]
72 --- 85 | cost [36.0]
73 --- 74 | cost [42.0]
74 --- 75 | cost [36.0]
75 --- 76 | cost [24.0]
76 --- 77 | cost [39.0]
77 --- 78 | cost [33.0]
79 --- 80 | cost [33.0]
80 --- 81 | cost [39.0]
81 --- 82 | cost [33.0]
82 --- 83 | cost [30.0]
83 --- 84 | cost [30.0]
84 --- 97 | cost [42.0]
85 --- 86 | cost [42.0]
86 --- 87 | cost [27.0]
87 --- 88 | cost [45.0]
88 --- 89 | cost [21.0]
89 --- 90 | cost [42.0]
90 --- 91 | cost [33.0]
91 --- 104 | cost [42.0]
92 --- 93 | cost [30.0]
92 --- 105 | cost [39.0]
93 --- 94 | cost [30.0]
94 --- 95 | cost [33.0]
95 --- 96 | cost [30.0]
96 --- 97 | cost [39.0]
98 --- 99 | cost [39.0]
98 --- 111 | cost [39.0]
99 --- 100 | cost [36.0]
100 --- 101 | cost [18.0]
101 --- 102 | cost [36.0]
102 --- 103 | cost [39.0]
103 --- 104 | cost [33.0]
105 --- 106 | cost [45.0]
106 --- 107 | cost [33.0]
107 --- 108 | cost [42.0]
108 --- 109 | cost [33.0]
109 --- 110 | cost [30.0]
110 --- 122 | cost [51.0]
111 --- 112 | cost [36.0]
112 --- 113 | cost [33.0]
113 --- 114 | cost [24.0]
114 --- 115 | cost [39.0]
115 --- 116 | cost [24.0]
116 --- 117 | cost [33.0]
117 --- 130 | cost [78.0]
118 --- 119 | cost [39.0]
118 --- 131 | cost [51.0]
119 --- 120 | cost [33.0]
120 --- 121 | cost [45.0]
121 --- 122 | cost [24.0]
123 --- 124 | cost [36.0]
123 --- 135 | cost [48.0]
124 --- 125 | cost [33.0]
125 --- 126 | cost [27.0]
126 --- 127 | cost [27.0]
127 --- 128 | cost [45.0]
128 --- 129 | cost [21.0]
129 --- 142 | cost [39.0]
130 --- 143 | cost [42.0]
131 --- 132 | cost [36.0]
132 --- 133 | cost [30.0]
133 --- 134 | cost [30.0]
134 --- 147 | cost [33.0]
135 --- 136 | cost [33.0]
136 --- 137 | cost [33.0]
137 --- 138 | cost [30.0]
138 --- 139 | cost [30.0]
139 --- 140 | cost [30.0]
140 --- 141 | cost [36.0]
141 --- 154 | cost [39.0]
142 --- 143 | cost [36.0]
144 --- 145 | cost [21.0]
144 --- 158 | cost [57.0]
145 --- 146 | cost [45.0]
146 --- 160 | cost [39.0]
147 --- 148 | cost [27.0]
148 --- 149 | cost [36.0]
149 --- 150 | cost [39.0]
150 --- 151 | cost [27.0]
151 --- 152 | cost [39.0]
152 --- 153 | cost [27.0]
153 --- 166 | cost [30.0]
154 --- 155 | cost [36.0]
155 --- 156 | cost [33.0]
156 --- 169 | cost [69.0]
157 --- 158 | cost [27.0]
157 --- 170 | cost [51.0]
159 --- 160 | cost [33.0]
159 --- 172 | cost [36.0]
161 --- 162 | cost [36.0]
161 --- 175 | cost [57.0]
162 --- 163 | cost [24.0]
163 --- 164 | cost [24.0]
164 --- 165 | cost [42.0]
165 --- 166 | cost [24.0]
167 --- 168 | cost [39.0]
167 --- 180 | cost [24.0]
168 --- 169 | cost [42.0]
170 --- 171 | cost [42.0]
171 --- 183 | cost [48.0]
172 --- 173 | cost [39.0]
173 --- 174 | cost [24.0]
174 --- 175 | cost [27.0]
176 --- 177 | cost [21.0]
176 --- 190 | cost [60.0]
177 --- 178 | cost [39.0]
178 --- 179 | cost [33.0]
179 --- 192 | cost [39.0]
180 --- 181 | cost [36.0]
181 --- 182 | cost [33.0]
182 --- 195 | cost [51.0]
183 --- 184 | cost [36.0]
184 --- 185 | cost [27.0]
185 --- 186 | cost [30.0]
186 --- 187 | cost [33.0]
187 --- 188 | cost [36.0]
188 --- 189 | cost [48.0]
189 --- 190 | cost [18.0]
191 --- 192 | cost [33.0]
191 --- 193 | cost [51.0]
193 --- 194 | cost [30.0]
194 --- 195 | cost [42.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 14 Jan 2024 06:11:37 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 196 hubs —— 1-2-3-4-5-6-7-8-9-10-11-12-13-24-23-25-26-39-38-37-36-35-34-22-21-20-19-18-31-32-33-46-47-48-49-50-51-52-65-64-63-62-61-60-59-57-58-71-72-73-74-75-76-77-78-91-90-89-88-87-86-85-84-97-98-99-100-101-102-103-104-117-116-115-128-129-130-143-142-141-140-139-138-137-150-151-164-163-162-161-160-159-172-173-174-175-176-177-178-179-165-166-153-152-154-155-156-169-168-167-180-181-182-195-194-193-192-191-190-189-188-187-186-185-184-183-171-170-157-158-144-145-146-147-148-149-136-135-134-133-132-131-118-119-120-121-122-123-124-125-126-127-114-113-112-111-110-109-108-107-106-105-92-93-94-95-96-83-82-81-80-79-66-67-68-70-69-55-54-53-40-41-42-43-56-45-44-30-29-17-16-15-28-27-14-196-1
total time           3604.6 (TL 3600)     gap                  0.024                
blossom time         0                    nb blossom           0.0                  
LB <= UB             6947<=7119           Master/SP costs      7119/0               
Master time          3604.6               SP time              0.0                  
subtour              22579.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       6350                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—3—4—5—6—7—8—9—10—11—12—13—24—23—25—26—39—38—37—36—35—34—22—21—20—19—18—31—32—33—46—47—48—49—50—51—52—65—64—63—62—61—60—59—57—58—71—72—73—74—75—76—77—78—91—90—89—88—87—86—85—84—97—98—99—100—101—102—103—104—117—116—115—128—129—130—143—142—141—140—139—138—137—150—151—164—163—162—161—160—159—172—173—174—175—176—177—178—179—165—166—153—152—154—155—156—169—168—167—180—181—182—195—194—193—192—191—190—189—188—187—186—185—184—183—171—170—157—158—144—145—146—147—148—149—136—135—134—133—132—131—118—119—120—121—122—123—124—125—126—127—114—113—112—111—110—109—108—107—106—105—92—93—94—95—96—83—82—81—80—79—66—67—68—70—69—55—54—53—40—41—42—43—56—45—44—30—29—17—16—15—28—27—14—196

RING
1  ---  2 | cost [42.0]
2  ---  3 | cost [21.0]
3  ---  4 | cost [33.0]
4  ---  5 | cost [39.0]
5  ---  6 | cost [21.0]
6  ---  7 | cost [39.0]
7  ---  8 | cost [39.0]
8  ---  9 | cost [33.0]
9  --- 10 | cost [24.0]
10 --- 11 | cost [39.0]
11 --- 12 | cost [27.0]
12 --- 13 | cost [24.0]
13 --- 24 | cost [63.0]
14 --- 27 | cost [48.0]
14 --- 196 | cost [60.0]
15 --- 16 | cost [33.0]
15 --- 28 | cost [42.0]
16 --- 17 | cost [21.0]
17 --- 29 | cost [51.0]
18 --- 19 | cost [42.0]
18 --- 31 | cost [51.0]
19 --- 20 | cost [39.0]
20 --- 21 | cost [30.0]
21 --- 22 | cost [33.0]
22 --- 34 | cost [42.0]
23 --- 24 | cost [27.0]
23 --- 25 | cost [54.0]
25 --- 26 | cost [36.0]
26 --- 39 | cost [45.0]
27 --- 28 | cost [36.0]
29 --- 30 | cost [33.0]
30 --- 44 | cost [54.0]
31 --- 32 | cost [21.0]
32 --- 33 | cost [39.0]
33 --- 46 | cost [42.0]
34 --- 35 | cost [42.0]
35 --- 36 | cost [30.0]
36 --- 37 | cost [18.0]
37 --- 38 | cost [42.0]
38 --- 39 | cost [36.0]
40 --- 41 | cost [27.0]
40 --- 53 | cost [27.0]
41 --- 42 | cost [36.0]
42 --- 43 | cost [27.0]
43 --- 56 | cost [33.0]
44 --- 45 | cost [24.0]
45 --- 56 | cost [63.0]
46 --- 47 | cost [24.0]
47 --- 48 | cost [33.0]
48 --- 49 | cost [39.0]
49 --- 50 | cost [48.0]
50 --- 51 | cost [30.0]
51 --- 52 | cost [27.0]
52 --- 65 | cost [75.0]
53 --- 54 | cost [39.0]
54 --- 55 | cost [36.0]
55 --- 69 | cost [54.0]
57 --- 58 | cost [30.0]
57 --- 59 | cost [48.0]
58 --- 71 | cost [30.0]
59 --- 60 | cost [48.0]
60 --- 61 | cost [21.0]
61 --- 62 | cost [39.0]
62 --- 63 | cost [27.0]
63 --- 64 | cost [36.0]
64 --- 65 | cost [24.0]
66 --- 67 | cost [27.0]
66 --- 79 | cost [39.0]
67 --- 68 | cost [27.0]
68 --- 70 | cost [57.0]
69 --- 70 | cost [24.0]
71 --- 72 | cost [33.0]
72 --- 73 | cost [27.0]
73 --- 74 | cost [42.0]
74 --- 75 | cost [36.0]
75 --- 76 | cost [24.0]
76 --- 77 | cost [39.0]
77 --- 78 | cost [33.0]
78 --- 91 | cost [75.0]
79 --- 80 | cost [33.0]
80 --- 81 | cost [39.0]
81 --- 82 | cost [33.0]
82 --- 83 | cost [30.0]
83 --- 96 | cost [69.0]
84 --- 85 | cost [36.0]
84 --- 97 | cost [42.0]
85 --- 86 | cost [42.0]
86 --- 87 | cost [27.0]
87 --- 88 | cost [45.0]
88 --- 89 | cost [21.0]
89 --- 90 | cost [42.0]
90 --- 91 | cost [33.0]
92 --- 93 | cost [30.0]
92 --- 105 | cost [39.0]
93 --- 94 | cost [30.0]
94 --- 95 | cost [33.0]
95 --- 96 | cost [30.0]
97 --- 98 | cost [36.0]
98 --- 99 | cost [39.0]
99 --- 100 | cost [36.0]
100 --- 101 | cost [18.0]
101 --- 102 | cost [36.0]
102 --- 103 | cost [39.0]
103 --- 104 | cost [33.0]
104 --- 117 | cost [63.0]
105 --- 106 | cost [45.0]
106 --- 107 | cost [33.0]
107 --- 108 | cost [42.0]
108 --- 109 | cost [33.0]
109 --- 110 | cost [30.0]
110 --- 111 | cost [39.0]
111 --- 112 | cost [36.0]
112 --- 113 | cost [33.0]
113 --- 114 | cost [24.0]
114 --- 127 | cost [33.0]
115 --- 116 | cost [24.0]
115 --- 128 | cost [72.0]
116 --- 117 | cost [33.0]
118 --- 119 | cost [39.0]
118 --- 131 | cost [51.0]
119 --- 120 | cost [33.0]
120 --- 121 | cost [45.0]
121 --- 122 | cost [24.0]
122 --- 123 | cost [33.0]
123 --- 124 | cost [36.0]
124 --- 125 | cost [33.0]
125 --- 126 | cost [27.0]
126 --- 127 | cost [27.0]
128 --- 129 | cost [21.0]
129 --- 130 | cost [36.0]
130 --- 143 | cost [42.0]
131 --- 132 | cost [36.0]
132 --- 133 | cost [30.0]
133 --- 134 | cost [30.0]
134 --- 135 | cost [39.0]
135 --- 136 | cost [33.0]
136 --- 149 | cost [42.0]
137 --- 138 | cost [30.0]
137 --- 150 | cost [48.0]
138 --- 139 | cost [30.0]
139 --- 140 | cost [30.0]
140 --- 141 | cost [36.0]
141 --- 142 | cost [42.0]
142 --- 143 | cost [36.0]
144 --- 145 | cost [21.0]
144 --- 158 | cost [57.0]
145 --- 146 | cost [45.0]
146 --- 147 | cost [39.0]
147 --- 148 | cost [27.0]
148 --- 149 | cost [36.0]
150 --- 151 | cost [27.0]
151 --- 164 | cost [39.0]
152 --- 153 | cost [27.0]
152 --- 154 | cost [54.0]
153 --- 166 | cost [30.0]
154 --- 155 | cost [36.0]
155 --- 156 | cost [33.0]
156 --- 169 | cost [69.0]
157 --- 158 | cost [27.0]
157 --- 170 | cost [51.0]
159 --- 160 | cost [33.0]
159 --- 172 | cost [36.0]
160 --- 161 | cost [42.0]
161 --- 162 | cost [36.0]
162 --- 163 | cost [24.0]
163 --- 164 | cost [24.0]
165 --- 166 | cost [24.0]
165 --- 179 | cost [69.0]
167 --- 168 | cost [39.0]
167 --- 180 | cost [24.0]
168 --- 169 | cost [42.0]
170 --- 171 | cost [42.0]
171 --- 183 | cost [48.0]
172 --- 173 | cost [39.0]
173 --- 174 | cost [24.0]
174 --- 175 | cost [27.0]
175 --- 176 | cost [39.0]
176 --- 177 | cost [21.0]
177 --- 178 | cost [39.0]
178 --- 179 | cost [33.0]
180 --- 181 | cost [36.0]
181 --- 182 | cost [33.0]
182 --- 195 | cost [51.0]
183 --- 184 | cost [36.0]
184 --- 185 | cost [27.0]
185 --- 186 | cost [30.0]
186 --- 187 | cost [33.0]
187 --- 188 | cost [36.0]
188 --- 189 | cost [48.0]
189 --- 190 | cost [18.0]
190 --- 191 | cost [48.0]
191 --- 192 | cost [33.0]
192 --- 193 | cost [36.0]
193 --- 194 | cost [30.0]
194 --- 195 | cost [42.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1